Welcome to the Bunnings Workshop community @Ginamach. It's fabulous to have you join us and many thanks for your question.
You could potentially use GRUNT 6mm x 10m Sisal Twisted Rope and re-weave the rope sections of the chair. It looks like they might have originally used some type of seagrass rope. It really depends on how intricately it has been woven.
Let me mention the wonderful @prettyliving and @Tara86 to see if they had any ideas on how you could restore these chairs.